The Doppler Effect

The effect that changed the world

Visionary that he was, even in his wildest dreams Christian Doppler could not possibly have imagined the importance his discovery would have for the whole of humanity, and the waves that his 1842 work “On the coloured light of binary stars and other stars of the heavens” would make. No other physical principle has changed our conception of the world as profoundly as the Doppler effect.

Quotes regarding the Doppler-Effect:
At a 2003 symposium in Salzburg to mark the 200th birthday of Christian Doppler, Professor. Anton Zeilinger, President of the Austrian Academy of Sciences, declared the Doppler-effect “the effect of the millennium.”
Albert Einstein, 1906: “Regardless of what form the theory of electromagnetic processes will take, the Doppler principle will certainly remain.”

Explanatory Video (German)

Der Doppler-Effekt

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The physics of the Doppler Effect.

The Doppler effect describes how the frequency of a wave changes according to how the emitter or receiver of the wave is moving The classical example used to explain the Doppler effect is that of an ambulance driving past an observer. The movement of the ambulance causes the sound waves in front of the ambulance to become compressed, and those behind it to be stretched. The observer perceives this effect as a change in the pitch of the siren. As the ambulance travels towards the observer, the pitch is higher. As soon as the ambulance starts to move away, the pitch becomes lower.

Der Doppler Effekt: Einsatzfahrzeug mit Schallwellen

This change in wave frequency is greater or smaller depending on whether the signal emitter and / or receiver is moving in a given medium – for example, in air. In his 1842 publication “On the coloured light of binary stars and other stars of the heavens”, Doppler provided the following formula for calculating the frequency perceived by an observer.

This formula includes
   the frequency perceived by the receiver
   the frequency given out by its emitter
   the speed of the receiver relative to the medium in which it is situated
   the speed of the emitter relevant to the medium in which it is situated
  the propagation speed of the wave in its medium (wave speed)

Situation 1: The receiver is stationary, the emitter is moving:

Situation 2: The emitter is stationary, the receiver is moving:

These two equations describe the classical Doppler effect. How the frequency changes thus depends upon the speed with which emitter and receiver are travelling relative to the transmission medium of the wave. This represented a revolutionary finding in Doppler’s time. Thus Doppler writes in his original work: “It is from these purely subjective conditions, and not from objective facts, that the perception of colour and intensity of light, or pitch and strength of a wave depends.”

Light and the Doppler effect

Christian Doppler speculated that this effect was valid for all types of wave. The scientific understanding at the time was that light required a transmission medium. The qualities of this medium were unknown, and it was referred to as “the ether”. It was only in 1881 and 1887 that the physicists Albert A. Michelson and Edward W. Morley were able to prove by experiment that there was no such ether that acted as a transmission medium for light (the Michelson-Morley experiment). Today we know that the classical Doppler effect only applies to waves that propagate within a medium.

CC: Tanja Kühnel / aus dem Buch
CC: Tanja Kühnel / from the book “Christian Doppler –Der für die Menschheit bedeutendste Salzburger” by Clemens M. Hutter

There is, however, also a Doppler effect for electromagnetic waves like light, which do not require a transmission medium. This is at the origin of colour shifts – towards blue when the emitter is moving towards the receiver and the waves are “squashed”, and towards red when the emitter is moving away, and the waves become “stretched” (see diagram).

In the case of electromagnetism, this effect is not dependent on the relative movement between the transmission medium and the receiver or emitter, but on the relative movement between receiver and emitter. For this reason, the Doppler effect for light waves is referred to as the relativistic Doppler effect. In the case of electromagnetic waves, the received frequency and the emitted frequency are given as follows:

In this formula for the relativistic Doppler effect, c represents the speed of light, at 299 792 km/s, and the relative speed of movement between emitter and receiver.

Practical applications of the Doppler formula

The following examples present two special cases of the propagation of a sound wave in air, where the frequency and speed of the movement variables explained above are plugged into the formula.

Situation 1: The receiver is stationary relative to the air, the emitter (source of the sound wave) is moving towards the receiver (-) or away from the receiver (+).

In this case the Doppler formula is:

For example: a car (sound wave emitter) travels at 130 km/h (~36 m/s) past a pedestrian standing at the side of the road (sound wave receiver). The driver and the pedestrian know each other, so the driver greets the pedestrian with a long honk on the horn. The pitch of the horn is 1 000 Hertz. What pitch does the pedestrian perceive?

Der Doppler Effekt: Ausbreitung der Schallwellen

As the car is approaching, the pedestrian hears a frequency of:

When the car moves away from the receiver, the pitch drops to:

In this way, as the car approaches, the pitch rises by 118 Hertz and then drops by 96 Hertz as the car moves away from the pedestrian. 1 000 Hertz corresponds to “high C”, the note found two lines above the typical five-line musical stave.  In this example, the changes in pitch during the car’s approach and as it moves away are small, and represent only about one semi-tone.

Situation 2: The emitter (source of the sound wave) is stationary relative to the air and the receiver is moving towards the emitter (+) or away from the emitter (-).

In this case the Doppler formula is:

For example: the car driver is now the receiver, and travels past their acquaintance standing at the roadside at 130 km/h (~36 m/s). By chance, the pedestrian has a horn with him, and greets the car driver with a long honk of the horn at a frequency of 1000 Hertz.

Approaching the pedestrian, the driver hears a note with a frequency of:

Moving away from the pedestrian, the driver hears a note with a frequency of:

In this scenario, the change in pitch perceived by the receiver (the driver) as they approach and move away from their acquaintance with the horn is the same, i.e. it goes up and down by 106 Hertz.

The reason for the difference in the changes in frequency in these two scenarios is that waves require a transmission medium, which in these cases is the air. In the first scenario, the emitter (the source of the soundwave) moves relative to the air, whereas in the second scenario it is the receiver who moves.

Based on the book:

Christian Doppler – Der für die Menschheit bedeutendste Salzburger, Clemens M. Hutter, Verlag Anton Pustet 2017